Kinematics Problem

Question

In a 100 m race, a sprinter accelerates for the first 40.0 m at 2.56 m/s(squared). After this distance he reaches top speed and maintains this speed for the rest of the race.

How long does it take the sprinter to run the first 40 m?

How long does he take to run the entire race?

Answer 1

First question:

Since he starts from rest at x=0,

d = at²/2 ⇒

t = √(2a/d)

Plug in d=40.0m and a=2.56m/s², and get t in seconds.

Second question:

Find the speed at the end of the 40.0 m run.

v = at

Plug in a=2.56m/s² and the result for t from the first question, and get v. Then calculate

t₁ = (100m - 40.0m) / v

The time to run the entire race is t+t₁.